Help! Favorite days out in London for a 1 year old

DH and I have got next Thurs and Fri off work, we were going to take DD away for a long weekend to somewhere lovely and child friendly. Babington is blimmin booked as is blasted Bruern, Moonfleet only has tiny rooms left and it's all so expensive anyway. Could go to NY for the weekend for the price of one there.

So, we have decided to have a holiday in London! Much less hassle, no travelling or packing and the nanny can do evenings instead of days so we can go out and have some fun too.

So, you guessed it, what can we do with DD that she will really enjoy? (she was 1 last week)

My ideas so far

Aquarium
National Gallery or Tate Modern (will she like that or is she too young?)
Riverbus
Lunch at the Oxo Tower for lovely view
City Farm (anyone know one?)
errr, that's it

She really adores music so anything with a musical bias would be a bonus.

Personally, as she is so young, I'd do exactly what you'd like to do as long as it is reasonably baby friendly. She won't remember any of it but you will! My ds is nearly two and still prefers the park and looking at and touching our artist-designed local bollards (yes, really, this is regenerated Peckham and they are by sculptor Anthony Gormley) to anything special we do
for him. Having said that, he seemed quite entertained by the riverbus last summer and we enjoyed it (Greenwich), and the Tate modern provides good running about space and is child-friendly. In my experience they like the oddest things. Ds was passionate about the black and white marble floors at Greenwich Palace - kept running around the circular pattern. At that age I do think though you should please yourself first, and your dd will enjoy coming along for the ride. This weekend we went to the Courtauld Gallery where he liked walking about, a big African mask and the air-conditioning which came out of ducts on the floor, which you could lay on and feel the wind on different bits of your body (!). But he just adored the fountains just outside at Somerset House, which are fantastic. You can walk amoung them as the water comes straight out of the ground and the fountains vary in height. Wwll worth a visit, particularly if you exploring the South Bank or Covent Garden.

Depending where you are in London the Horniman Museum (Forest Hill) is fab for kiddies. I thought of it because of the music stuff - there is a room where kiddies can put on headphones and press buttons to hear different instruments playing. It's designed for older kids, but my dd (13 months) seemed to love it. There's also a 'hands on' music room where they can bash a few drums, play plastic tubes with flip flops, have a go on a stringed plucky instrument thingy! Also there's a little aquarium built at kiddie level, loads of stuffed animals, lovely gardens complete with goat! And a child-friendly cafe, plus a conservatory where you can take your own picnic and still have tables, highchair etc. And it's free.

Tate Modern is also great - loads of crawling space. And they're baby friendly in the cafe. One of the (Italian) waiters even came over and tickled my dd's feet whilst she was breastfeeding. How many british men would have done that!?

We took DS to Vauxhall City Farm at one, and he loved it, there's also a v good one at Surrey Docks. Also the little zoo in Battersea Park, which also has fountains etc.
And check Time Out: some enterprising Children's Theatre Companies are now doing shows for 6m plus! Quite interactive and touchy-feely - but they only crop up occasionally. (I think Polka theatre have one the w/e of 18/19 Oct). My DS also enjoyed Tate Modern - there's a gallery which is all about art which relates to us physically (or something): tiles which can be crawled on, shiny reflective sculptures, Rachel Whiteread installation which is good for pulling up on and cruising around!
We spent the Easter break doing a different London Park each day: Dulwich and Clapham Common have great cafes which serve alcohol, too (Oom Pah Pah by the bandstand in Clapham.
Also took DS on The Eye at one...the confined space, with other passengers, wasn't a great success!

Although it's not particularily cheap, the London Transport Museum in Covent Gdn has a small play area with trains and a play train you can climb on and lots of real buses and trains. Handy if you want to fit some shopping in too! My ds loves it (admittedly I took him there for the first time when he was nearly 2)

The Princess DIana memorial playground in Kensington Gardens (up by Kensington Palace) is really nice with a huge sandpit. It also has a big wooden pirate ship to climb on but I think your DD will be a bit young for that. DSs had great fun there.

Ok, another one. Which good restaurants in town allow babies in at lunchtime? We want to go for a really good lunch but afraid everywhere will be full of disapproving suits etc. Anyone know somewhere with GOOD food who will allow small monsters in?

We also had a great time in the Tate Modern, especially with the waiters in the cafe . DD also enjoyed crawling around in one of the millenium wheels capsules - but pick a very qiet time, and don't do it if the sight of your D child sillouteeted against london ({far below) would freak you out!! We didn't brave many restaurants but had a great brunch at Carluccios (near Canary Wharf UG) - more baby friendly Italians, lots of homemade breadsticks (gnawing food), good selection of papers (took it in turns) and hot chocolate that was so chocolately you had to eat it with a spoon.

Babylon at the Hanging Gardens (99 Kensington Highstreet) have baby changing facilities so I assume they are happy to have children. No idea whether they offer high chairs or children's food/portions though. Went there yesterday lunchtime and it was not very busy at all.

The cafe at the Wallace Gallery has nice food and good baby changing facilities, lots of space between tables as well + it is close to Selfridges, which DS likes in small doses, as there is generally something interesting to look at. Somebody I know also recommended the People's Palace - partly because it is often very empty! But also for the great view of the Thames, complete with trains, boats and buses. I have only been to the Carluccios cafe in Kingston but it was very child-friendly (breadsticks on demand, toys to play with, highchairs etc) and food came quickly - a consideration with short attention spans. If you do go out to Leatherhead for Bocketts Farm, DS loves Polesden Lacey - rolling down the hill mostly. DS also loves trains, riding escalators and listening to buskers on the tube!